Glad to find this thread!
I've been an RN for less than a year, but my church was involved in a medical mission trip to Honduras last year, I went and loved it so much I'm going back this year! We teamed with an organization called World Gospel Outreach http://www.wgoreach.org/
who routinely host "medical brigades." There were positions for lay people as well.
A Honduran doctor was with us and available for consultation, but basically we had 7 medication stations where we heard complaints thru translators, and dispensed medication via a donated pharmacy that traveled with us. It was incredible, and the people were so greatful. My spanish also got a great crash course!
I know there are many organizations out there, I hope you find one you enjoy. Several of my nursing instructors in school also did medical trips, their best advice: make sure it is a reputable organization.
Good luck and God bless!